The present invention relates to photonic band gap (PBG) materials and methods of production, and more particularly the present invention describes a set of new classes of photonic crystal structures which exhibit large and complete three-dimensional PBGs and which are amenable to large scale micro-fabrication.
Photonics is the science of molding the flow of light. Photonic band gap (PBG) materials, as disclosed in S. John, Phys. Rev. Lett. 58, 2486 (1987), and E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987), are a new class of dielectrics which carry the concept of molding the flow of light to its ultimate level, namely by facilitating the coherent localization of light, see S. John, Phys. Rev. Lett. 53, 2169 (1984), P. W. Anderson, Phil. Mag. B 52, 505 (1985), S. John, Physics Today 44, no. 5, 32 (1991), and D. Wiersma, D. Bartolini, A. Lagendijk and R. Righini, Nature 390, 671 (1997). This provides a mechanism for the control and inhibition of spontaneous emission of light from atoms and molecules forming the active region of the PBG materials, and offers a basis for low threshold micro-lasers and novel nonlinear optical phenomena. Light localization within a PBG facilitates the realization of high quality factor micro-cavity devices and the integration of such devices through a network of microscopic wave-guide channels (see J. D. Joannopoulos, P. R. Villeneuve and S. Fan, Nature 386,143 (1998)) within a single all-optical microchip. Since light is caged within the dielectric microstructure, it cannot scatter into unwanted modes of free propagation and is forced to flow along engineered defect channels between the desired circuit elements.
PBG materials, infiltrated with suitable liquid crystals, may exhibit fully tunable photonic band structures [see K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1999) and E. Yablonovitch, Nature 401, 539 (1999)] enabling the steering of light flow by an external voltage. These possibilities suggest that PBG materials may play a role in photonics, analogous to the role of semiconductors in conventional microelectronics. As pointed out by Sir John Maddox, xe2x80x9cIf only it were possible to make dielectric materials in which electromagnetic waves cannot propagate at certain frequencies, all kinds of almost magical things would be possible.xe2x80x9d John Maddox, Nature 348, 481 (1990).
The four major categories of 3-d PBG materials, which have been disclosed, can be classified according to the frequency bands between which a full photonic band gap appears. The number of frequency bands below the full PBG depends on the size of the unit cell in which the periodic (repeating) lattice structure is defined. For example, a lattice with a given periodically repeated unit cell can be alternatively described with a larger unit cell which has twice the size (volume) of the originally chosen unit cell. In the second (equivalent) description, the number of bands that appears below the full photonic band gap would be double the number of bands that appears below the full PBG in the original description and each of the bands in the second description would contain half the number of electromagnetic modes when compared to the bands in the original description. In identifying the categories of 3D PBG materials, we exclude categories that arise purely from such changes in the definition of the unit cell. By making use of the smallest possible unit cell for a given photonic crystal structure, we identify four distinct categories of PBG materials disclosed previously:
In the first category (category 1) are PBG materials which exhibit a complete PBG between the eighth and ninth bands of the photonic band structure. This includes the Bravais (one scatterer per unit cell) lattices of spheres such as the face centered cubic (FCC) lattice, the hexagonal close packed (HCP) lattice, the body centered cubic (BCC) lattice, and minor variations of these structures. These PBG materials generally exhibit a small (less than 10%) PBG between the eighth and ninth bands but are accompanied by large pseudo-gaps (a frequency range in which the photon density of states is strongly suppressed but does not vanish) between lower bands. This category entails the widely studied inverse opal structures, see for instance S. John and K. Busch, IEEE Journal of Lightwave Technology 17,1931 (1999). The PBG materials associated with category one generally have gaps which are not robust and which collapse under moderate amounts of disorder. On the other hand, the high sensitivity of this PBG to small perturbations can be utilized to achieve complete tunability of the gap as disclosed by K. Busch and S. John, Physical Review Letters 83, 967 (1999).
In the second category (category 2), are PBG materials which exhibit a complete gap between the second and third bands (sometimes referred to as the fundamental gap) of the photonic band structure. This includes the diamond lattice of spheres, the inverse diamond lattice (see K. M. Ho, C. T. Chan, and C. M. Soukoulis, Physical Review Letters 65, 3152 (1990)), the tetrahedral network of rods on a diamond lattice (see C. T. Chan, S. Datta, K. M. Ho, and C. M. Soukoulis, Physical Review B 50,1988 (1994)), the Yablonovite structure (see E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Physical Review Letters 67, 2295 (1991)), and the woodpile structure (see S. Y. Lin and J. G. Fleming, IEEE Journal of Lightwave Technology 17,1944 (1999) and S. Noda et. al IEEE Journal of Lightwave Technology 17,1948 (1999)). PBG materials in this category generally have very large gaps (20%-30%) and the gap is highly robust to disorder effects. However, micro-fabrication of category 2 structures has thus far been very limited due to complexity and expense.
In the third category (category 3) are PBG materials which exhibit a complete gap between the fifth and sixth bands of the photonic band structure. These include simple cubic mesh structures as disclosed by H. Sozuer and J. W. Haus, Journal of the Optical Society of America B 10, 296 (1993). All structures in category 3, which have been disclosed so far, exhibit relatively small (less than 10%) photonic band gaps.
In the fourth category (category 4) are PBG materials which exhibit a complete gap between the fourth and fifth bands of the photonic band structure.
Following the initial disclosure of the photonic band gap concept (S. John, Phys. Rev. Lett. 58, 2486 (1987), and E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987)), it was suggested that a diamond lattice of high refractive index spheres in air as well as the inverse diamond lattice , consisting of overlapping air spheres in a high refractive index background, would provide a large three-dimensional PBG, see K. M. Ho, C. T. Chan, and C. M. Soukoulis, Physical Review Letters 65, 3152 (1990). While the theoretical demonstration of a large PBG in the inverse diamond lattice was an important milestone in the field, the proposed structure has proven impractical from a micro-fabrication point of view. A number of structures, related to the inverse diamond lattice, were later proposed to circumvent the micro-fabrication barrier. These include the Yablonovite (see E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Physical Review Letters 67, 2295 (1991)) structure and the woodpile structure (see S. Y. Lin and J. G. Fleming, IEEE Journal of Lightwave Technology 17,1944 (1999) and S. Noda et. al IEEE Journal of Lightwave Technology 17,1948 (1999)). Each of these structures mimics the diamond lattice, and like the diamond lattice exhibits a large 3D PBG between the second and third bands in the photonic band structure. These structures belong to a different category from the inverse opal (face centered cubic lattice) structures which exhibit a comparatively small (5%-9% in the case of a silicon inverse opal) 3-d PBG between the eighth and the ninth bands of the photonic band structure.
In addition to these structures, a theoretical blueprint for certain circular spiral post structures has been disclosed, [see A. Chutinan and S. Noda Phys. Rev. B, 57, R2006-R2008 (1998)]. These circular spiral posts may be arrayed in either a body centered cubic (BCC), face centered cubic (FCC), or simple cubic (SC) lattice structure. The FCC and BCC structures, are based on visual similarity to the diamond lattice. In both of these structures, the spiral rods are arranged in a lattice but adjacent spiral rods are mutually half period shifted as the rods wind in the vertical direction. These structures are predicted to have a photonic band gap between the second and third bands in the photonic band structure. Chutinan and Noda have disclosed a particular set of geometrical parameters for which the FCC circular spiral photonic crystal exhibits a PBG which is comparable in size to the inverse diamond lattice. However, micro-fabrication of the FCC circular spiral structure has thus far been impractical. Novel deposition methods such as Glancing Angle Deposition (GLAD) [see K. Robbie and J. Brett, Nature 384, 616 (1996)] cannot be readily applied to this structure due to the half period shift between adjacent spiral rods. Another method involves three-dimensional lithography using a two-photon confocal microscope [see Cumpston et. al. Nature 398 51-54 (1999)]
Neither the FCC circular spiral nor the inverse diamond lattice have been synthesized up to now. The corresponding PBG for the BCC circular spirals is smaller than that of the FCC circular spirals and it also occurs between the second and third bands of the photonic band structure. However, micro-fabrication of the BCC circular spiral is also impractical for the same reasons stated for the FCC circular spiral. The simple cubic (SC) circular spiral structure is distinct from either the FCC or BCC circular spiral structures. In the SC circular spiral, the adjacent spiral rods are not half period shifted from each other and the PBG appears between the fourth and fifth bands of the photonic band structure rather than between the second and third bands. Chutinan and Noda have disclosed a 16.8% PBG in a SC circular spiral structure in which the background material has a dielectric constant of 12.25 and the rods consist of air. A tetragonal circular spiral structure can be visualized by considering the SC circular spiral structure and stretching the spiral rods along the vertical direction such that the periodicity in the vertical direction no longer coincides with the periodicity in the plane perpendicular to the rod axes. Chutinan and Noda have disclosed only one case of a tetragonal circular spiral structure for which the PBG (of 3%) is negligibly small. An attempt to improve on the Chutinan-Noda structure has been disclosed by Y-C. Tsai, J. B. Pendry, and K. W-K. Shung, Physical Review B 59, R10401 (1999) using various woven dielectric fiber structures. However, the maximum gaps disclosed in this improvement are no larger than 7%.
The present invention relates to photonic band gap (PBG) materials and more specifically, it describes a set of new classes of photonic crystal structures which exhibit a large and complete three-dimensional PBG. This PBG is highly robust to the effects of disorder. The photonic crystal has a tetragonal or other lattice symmetry and is comprised of a lattice of square or other polygonal spiral posts of a high refractive index material in a low index background. The corresponding inverse structure comprised of a lattice of low refractive index posts in a high refractive index background also has a very large PBG .
In the present invention, the inventors present for the first time a process for producing a broad range of spiral structures exhibiting very large complete 3-d photonic band gaps (up to 23.6% when made of silicon and nearly 29% when made of germanium). In a preferred embodiment of the present invention the posts exhibit a square spiral profile. All the square spiral posts wind in phase with each other i.e. there is no phase shift between adjacent rods. The identity of the winding phase from one post to the next makes the present invention amenable to micro-fabrication using the GLAD method. In a non-limiting example of the present invention, there is provided a three-dimensional lattice having tetragonal symmetry and a PBG occurs between the fourth and fifth bands of the photonic band structure. The present invention is a major new development in the identification of PBG materials with large photonic band gaps in the near-infrared (1.5 micron wavelength) and visible spectral regions and which are amenable to inexpensive, rapid, large scale manufacturing. We disclose, for the first time, a set of novel, broad ranges of specific geometrical parameters for micro-fabrication of materials with a very large PBG. These crystals can be fabricated using a technique called Glancing Angle Deposition (GLAD), [see K. Robbie and J. Brett, Nature 384, 616 (1996)], or a technique involving two-photon confocal microscopy, [see Cumpston et. al. Nature 398 51-54 (1999)], but is not limited to these techniques. The present invention provides a blueprint whereby these or other techniques can be adapted to synthesize these new types of PBG materials. These materials have applications in a variety of lightwave technologies.
In one aspect of the invention there is provided a photonic crystal, comprising:
a three dimensional crystal lattice including a plurality of substantially square, triangular, or other multi-sided (polygonal) spiral posts having a first refractive index arranged in a material having a second refractive index, said three dimensional crystal lattice having tetragonal, hexagonal, or other symmetry; and said first and second refractive indexes being sufficiently different from each other so that said photonic crystal has a complete three-dimensional photonic band gap.
In another aspect of the invention there is provided a method of producing a photonic crystal, comprising a three dimensional crystal lattice including a plurality of substantially square, triangular, or other multi-sided (polygonal) spiral posts having a first refractive index arranged in a material having a second refractive index, said three dimensional crystal lattice having tetragonal or other symmetry, wherein said first and second refractive indexes are sufficiently different from each other so that said photonic crystal has a complete three-dimensional photonic band gap, the method comprising:
etching of a flat surface (substrate) with a two-dimensional periodic lattice of vertical seed posts whose height is roughly one-quarter of the spacing between the seed posts; said seed posts arranged in a square, triangular, honeycomb, or other lattice; orienting said substrate at a pre-selected angle to a vapor flux containing said first material such that said pre-selected angle facilitates a shadowing of the substrate by the seed posts and the subsequent exposure of the posts (and not the spaces between the posts) to the vapor flux, depositing said first material using glancing angle deposition onto said seed posts, rotating the substrate and seed posts at pre-selected time intervals and to pre-selected orientations , and thereby growing spiral posts comprising said first material which wind about a z-axis in phase with each other.
heating and compressing a photonic crystal template consisting of a lattice of spiral posts, depositing a further amount of said first material uniformly on all exposed surfaces of said spiral posts so as to increase the thickness of the arms of said spiral posts, infiltrating the air regions between the resulting spiral posts in a uniform manner with said second material, selectively etching (removing) said first material and thereby creating spiral posts comprising air embedded in said second material.